arXiv math/02070512002-07math.CAmath.CO

由三重相关重构函数

Reconstruction of functions from their triple correlations

Philippe Jaming, Mihail N. Kolountzakis

备注：: 17 pages, preprint. This is a generous revision of our paper with the same title that was posted on the Arxiv a year ago. This was necessary as we had missed a very significant article by Grunbaum and Moore. Much more has been proved in the real case and in the cyclic case some results complementgin those of Grunbaum and Moore have been proved

摘要：

设A是阿贝尔群G的子集.要知道A的3-deck就是要知道每个可能的多重集{0，a，b}的平移在A中的占用数。3-deck的概念自然地推广到G上的可积函数。在本文中，我们研究了当一个函数的3-deck决定的功能，直到翻译。方法是看函数的傅里叶变换。我们的重点是实直线和循环群。

英文摘要：

Suppose that A is a subset of an abelian group G. To know the 3-deck of A is to know the number of occurences in A of translates of each possible multiset {0,a,b}. The concept of the 3-deck is naturally extended to integrable functions on G. In this paper we study when the 3-deck of a function determines the function up to translations. The method is to look at the Fourier Transform of the function. Our emphasis is on the real line and the cyclic groups.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。